𝔖 Bobbio Scriptorium
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On nonlinear systems—chaos

✍ Scribed by Y.H. Ku; Xiaoguang Sun


Book ID
103091734
Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
598 KB
Volume
326
Category
Article
ISSN
0016-0032

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✦ Synopsis


Two nonlinear systems which exhibit chaotic characteristics are analysed with the aid of computer graphics. The first system is represented by the Lorenz equations involving three variables X, y and z. The second system is known as the double scroll given by an electric circuit involving the voltages V,, and V,,, and the current i,, with two capacitances C, and C2, an inductance L, one resistance G and a nonlinear resistor with piecewise Iinear characteristic. For the first system, projections of the 3-dimensional traj'ectory are given onto the z:x, z-y and y-x phase planes obtained with the aid of computer graphics. Similarly, the phase plane projections onto the x-x, jr-y and i-z planes are presented, with the projections onto the i-i, 9-i and i-9 phase $lanes. For the second system, one can get the projections onto the Vc,-i,, VcZ-iL and VcZ-Vc, phase planes. By suitable transformations the state equations jar the double scroll can be expressed in terms of the variables X, y and z. Projections onto the z-x, y-x and z-y phase planes are presented. Similarly, projections onto the i-x, jry and i-z phase planes are given, together with the projections onto the i-k, jl-jc and i-ji phase planes. The solution curves X, y and z for the Lorenz equations are shown. For the double scroll, x, y and z curves and their derivatives i, jl and i are also presented.


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